Question

The lines x=-y,z=2 and x=y,z=0 intersect each other?

Answer 1

The line  L1  :    x = - y  and  z = 2
                 L2 :  x = y  and  z = 0

       L1 and L2  are in two different 3-d  planes which are  z = 2 and z = 0.

They are in parallel planes and the distance between them is  2 units.  Thus they never intersect.